Solve (ii) a / (b - c) = a/b - a/c | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$a \div ( b - c ) = \frac { a } { b } - \frac { a } { c }$$

Solve for a

$a=0$
$b\neq c\text{ and }b\neq 0\text{ and }c\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $bc\left(-b+c\right)$, the least common multiple of $b-c,b,c$.

$$-bca=c\left(-b+c\right)a-b\left(-b+c\right)a$$

Use the distributive property to multiply $c$ by $-b+c$.

$$-bca=\left(-cb+c^{2}\right)a-b\left(-b+c\right)a$$

Use the distributive property to multiply $-cb+c^{2}$ by $a$.

$$-bca=-cba+c^{2}a-b\left(-b+c\right)a$$

Use the distributive property to multiply $b$ by $-b+c$.

$$-bca=-cba+c^{2}a-\left(-b^{2}+bc\right)a$$

Use the distributive property to multiply $-b^{2}+bc$ by $a$.

$$-bca=-cba+c^{2}a-\left(-b^{2}a+bca\right)$$

To find the opposite of $-b^{2}a+bca$, find the opposite of each term.

$$-bca=-cba+c^{2}a+b^{2}a-bca$$

Combine $-cba$ and $-bca$ to get $-2cba$.

$$-bca=-2cba+c^{2}a+b^{2}a$$

Add $2cba$ to both sides.

$$-bca+2cba=c^{2}a+b^{2}a$$

Combine $-bca$ and $2cba$ to get $bca$.

$$bca=c^{2}a+b^{2}a$$

Subtract $c^{2}a$ from both sides.

$$bca-c^{2}a=b^{2}a$$

Subtract $b^{2}a$ from both sides.

$$bca-c^{2}a-b^{2}a=0$$

Reorder the terms.

$$-ab^{2}+abc-ac^{2}=0$$

Combine all terms containing $a$.

$$\left(-b^{2}+bc-c^{2}\right)a=0$$

Divide $0$ by $-b^{2}+bc-c^{2}$.

$$a=0$$

Solve for b

$b\in \mathrm{R}\setminus c,0$
$a=0\text{ and }c\neq 0$